To solve for $\cosh x$ and $\sinh x$ given that $\tanh x = 13$, let's use the definition of hyperbolic functions and identities related to $\tanh x$:

Step-by-Step Solution

1. Definition of $\tanh x$: $\tanh x = \frac{\sinh x}{\cosh x}$ Given: $\tanh x = 13 = \frac{\sinh x}{\cosh x}$ This implies that: $\sinh x = 13 \cosh x$

2. Using the Hyperbolic Identity: Recall that: $\cosh^2 x - \sinh^2 x = 1$ Substitute $\sinh x = 13 \cosh x$ into this identity: $\cosh^2 x - (13 \cosh x)^2 = 1$ Simplify: $\cosh^2 x - 169 \cosh^2 x = 1$ $-168 \cosh^2 x = 1$ $\cosh^2 x = -\frac{1}{168}$

Since this yields a negative square, there appears to be an issue with the given $\tanh x = 13$, as $|\tanh x|$ is always less than 1. Please verify if there's a mistake in the initial condition, as $\tanh x = 13$ is not feasible with real hyperbolic functions.